Bending of Beams: Singularity Functions and Stress Analysis

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Explores beam bending, load deformation, and resistance, emphasizing the importance of shear and moment diagrams.

Covers the theory of beam bending, historical figures, moment-curvature relation, and implications of distributed loads.

Explores quadratic moment, relative strains in beams, and pure flexion, focusing on neutral axis, curvature, and normal stresses.

Explains the step-by-step process of calculating centroids and second moments of complex shapes using integration and the parallel axis theorem.

Explores simple shear, shear stress, strain energy, stress analysis, and torsional shear stress in simple twist.

Covers stress, strain tensors, material constants, and beam bending fundamentals.

Covers beams with distributed and concentrated forces, bending moment, shear force, and internal load diagrams.

Explains stresses and neutral axis in composite beams, demonstrating calculations and examples.

Covers systems of forces, moments, couples, and stress in 2D and 3D, as well as the effect of force-couple systems.

Introduces 3D linear elasticity, beams, dimensional analysis, and mechanics of slender structures.